Using the most recent cosmic ray spectra up to 2x10 to the 20th power eV, production spectra of high energy neutrinos from cosmic ray interactions with interstellar gas and extragalactic interactions of ultrahigh energy cosmic rays with 3K universal background photons are presented and discussed. Estimates of the fluxes from cosmic diffuse sources and the nearby quasar 3C273 are made using the generic relationship between secondary neutrinos and gammas and using recent gamma ray satellite data. These gamma ray data provide important upper limits on cosmological neutrinos. Quantitative estimates of the observability of high energy neutrinos from the inner galaxy and 3C273 above atmospheric background for a DUMAND type detector are discussed in the context of the Weinberg-Salam model with sq sin theta omega = 0.2 and including the atmospheric background from the decay of charmed mesons. Constraints on cosmological high energy neutrino production models are also discussed. It appears that important high energy neutrino astronomy may be possible with DUMAND, but very long observing times are required.